Put the eggs in a medium saucepan and cover them with water, about 1 to 2 inches above the eggs. Place the pan over medium heat and bring to a full boil. Place the lid on the pan and remove it from the heat. Let the eggs stand for 15 minutes.
Transfer the cooked eggs to a bowl of ice water to stop the cooking process.
Peel the eggs under cool running water and then cut them in half lengthwise. Pop the egg yolks into a small bowl and place the egg whites on a plate or egg tray.
Mash the yolks with a fork and then add the mayonnaise, mustard, salt, and pepper. Mix until well blended.
Fill the egg halves with the egg yolk mixture. Put the filled eggs in the refrigerator until you are ready to decorate the eggs.
Slice the olives in half and set aside 12 halves for the spider bodies. Slice the remaining halves into thin "legs" for the spiders.
Arrange 8 thin legs on a stuffed egg and place an olive half "body" in the center. Repeat with the remaining legs and olives. Move decorated eggs to a container and refrigerate them as you work on the remaining eggs.
Arrange the Halloween eggs on an egg tray or large plate and chill until serving time.